In the case of Kreiger v. Kreiger (1947), the United States Supreme Court was asked to determine whether a state court had jurisdiction over an alimony dispute involving parties who were no longer residents of that state. The couple in question, Mr. and Mrs. Kreiger, had divorced in California but both moved out of the state afterwards; Mrs. Krieger then sought enforcement of her alimony agreement from her ex-husband through a Nebraska court where she resided at that time. The Supreme Court ruled unanimously in favor of Mrs. Krieger, stating that once personal jurisdiction has been established by a court - as it was when they initially granted divorce and set up an alimony arrangement - it continues for as long as necessary to enforce judgments related to those matters even if neither party remains within its geographical boundaries. This decision clarified the extent to which courts can exercise their power beyond their physical jurisdictions especially regarding domestic relations cases such as divorce settlements and child custody arrangements.

In the dissenting opinion for Krieger v. Krieger, Justice Jackson disagreed with the majority's decision to uphold a lower court ruling that allowed Mrs. Krieger to collect alimony from her ex-husband who was living in Germany at the time of their divorce and had no assets in America. He argued that this case involved international law principles which should not be decided by state courts but rather by federal authorities or through diplomatic channels due to its potential impact on foreign relations. Furthermore, he contended that enforcing an American judgment abroad could lead other countries to enforce their judgments within U.S., potentially infringing upon our sovereignty and legal system.